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In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds to a linear system of algebraic equations with unknown Laguerre coefficients‎. ‎We prove the convergence analysis of method applied to the solution integro-differential equations‎. ‎Finally‎, ‎numerical examples illustrate the efficiency and accuracy of the method.